Question

Simplify using laws of exponents (1296)^-1/4

Answer 1

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Answer 2

Using laws of exponents the value of $(1296)^{-\frac{1}{4}}$ is $\frac{1}{6}$.

Given :

$(1296)^{-\frac{1}{4}}$

To find :

The value of $(1296)^{-\frac{1}{4}}$

Law of exponents :

Here we use the law of exponents for real numbers.

Let a be a real number and p, q be rational numbers, then

Some law of exponents are : $a^-^1 = \frac{1}{a}$ , $a^-^p = \frac{1}{a^p}$, $(a^p )^q = a^p^q$ , a⁰ = 1, (a × b)ⁿ = aⁿ × bⁿ

Solution :

Step 1 of 3 :

Using the law of exponents $a^-^p = \frac{1}{a^p}$

$(1296)^{-\frac{1}{4}} = \frac{1}{(1296)^{\frac{1}{4}}}$

Step 2 of 3:

Split 1296 into the fourth power of 6:

$\frac{1}{(1296)^{\frac{1}{4}}} = \frac{1}{(6^4)^{\frac{1}{4}}}$

Step 3 of 3:

Using the law of exponents $(a^p )^q = a^p^q$and Cancelling the powers

$\frac{1}{(6^4)^{\frac{1}{4}}} = \frac{1}{6^4\times^{\frac{1}{4}}} = \frac{1}{6}$

Hence, the value of $(1296)^{-\frac{1}{4}}$ is $\frac{1}{6}$.

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