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According to the exponent rules, to multiply two expressions with the same base, we add the exponents while the base remains the same. This means, 10 -3 × 10 4 = 10 (-3 + 4) = 10 1 = 10. Answer: 10. Example 2: Simplify the given expression and select the correct option using the laws of exponents: 10 15 ÷ 10 7. (a) 10 8.
- Fractional Exponents
In this case, along with a fractional exponent, there is a...
- Expression
An expression is a combination of terms that are combined by...
- Reciprocal
According to the reciprocal definition in math, the...
- Fractional Exponents
The whole expression 3 4 is said to be power. Also learn the laws of exponents here. Basically, power is an expression that shows repeated multiplication of the same number or factor. The value of the exponent is based on the number of times the base is multiplied to itself. See of the examples here:
- 3 min
- Power is an expression that represents the repeated multiplication of value or integer. In general, a n is a power where a is the base and n is the...
- If N is an integer and is raised to another integer, say ‘a’, then the whole expression, N^a, is the power and a is the exponent.
- The examples of exponents are: 2 x 2x 2 =2 3 (2 raised to 3rd power) 5x5x5x5 = 5 4 (5 raised to 4th power) 9x9x9x9x9 = 9 5 (9 raised to 5th power)
- The rules of exponents are: a 0 = 1 a m a n = a m+n a m /a n = a m-n (a m ) n = a mn
- A negative exponent is used when 1 is divided by repeated multiplication of a factor. Say, 1/n is given by n -1 , where -1 is the exponent. If a nu...
- If the exponent of a base number is one, then the value of the base remains unchanged. For example, 9 1 = 9 If the exponent is 0, then we get 1 as...
The power of a power rule in exponents is a rule that is applied to simplify an algebraic expression when a base is raised to a power, and then the whole expression is raised to another power. The rule states that 'If the base raised to a power is being raised to another power, then the two powers are multiplied and the base remains the same.'
The power of a power rule can be used if the base is raised to a power and the whole term is again raised to another power. The two powers can be multiplied without changing the base. Power of a power rule formula: (a m) n = a m n. Any non-zero base raised to the power 0 is 1. Power of a power rule is also termed as power to a power rule.
- $(x^{\frac{m}{n}})^{\frac{p}{q}} = x^{\frac{pm}{nq}}$
- If the base a is raised to a power m and the entire expression $a^{m}$ is again raised to the power n, then we keep the same base and multiply the...
- $a^{m} \times a^{n} = a^{m\timesn}$
- Power of a power rule: $(a^{m})^{n} = a^{mn}$ Negative Exponent Rule: $a^{-m} = \frac{1}{a^{m}}$
- The Key to The Laws
- All You Need to Know ...
- Laws Explained
- The Law That xmxn = Xm+N
- The Law That Xm/Xn = Xm-N
- The Law That Xm/N = N√Xm =(N√X )M
- And That Is It!
Writing all the letters down is the key to understanding the Laws So, when in doubt, just remember to write down all the letters (as many as the exponent tells you to) and see if you can make sense of it.
The "Laws of Exponents" (also called "Rules of Exponents") come from three ideas: If you understand those, then you understand exponents! And all the laws below are based on those ideas.
The first three laws above (x1 = x, x0 = 1 and x-1 = 1/x) are just part of the natural sequence of exponents. Have a look at this: Look at that table for a while ... notice that positive, zero or negative exponents are really part of the same pattern, i.e. 5 times larger (or 5 times smaller) depending on whether the exponent gets larger (or smaller...
With xmxn, how many times do we end up multiplying "x"? Answer: first "m" times, then by another"n" times, for a total of "m+n" times.
Like the previous example, how many times do we end up multiplying "x"? Answer: "m" times, then reduce thatby "n" times (because we are dividing), for a total of "m-n" times. (Remember that x/x = 1, so every time you see an x"above the line" and one "below the line" you can cancel them out.) This law can also show you why x0=1:
OK, this one is a little more complicated! I suggest you read Fractional Exponentsfirst, so this makes more sense. Anyway, the important idea is that: x1/n = The n-th Root of x And so a fractional exponent like 43/2 is really saying to do a cube (3) and a square root(1/2), in any order. Just remember from fractions that m/n = m × (1/n): The order d...
If you find it hard to remember all these rules, then remember this: you can work them out when you understand the three ideasnear the top of this page: 1. The exponent sayshow many timesto use the number in a multiplication 2. A negative exponent meansdivide 3. A fractional exponent like 1/n means totake the nth root: x(1n) = n√x
The power is an expression that shows repeated multiplication of the same number or factor. For example, in the expression 6 4, 4 is the exponent and 6 4 is called the 6 power of 4. That means, 6 is multiplied by itself 4 times. Learn more about exponents and powers here. Video Lesson. Watch The Below Video To Understand Exponents
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To simplify the power of a quotient of two expressions, we can use the power of a quotient rule, which states that the power of a quotient of factors is the quotient of the powers of the factors. For example, let’s look at the following example.
