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Ann [662]
3 years ago
5

Which expression is equivalent to (256x^16)^1/4 A.4x^2 B.4x^4 C. 64x^2 D. 64x^4

Mathematics
2 answers:
antiseptic1488 [7]3 years ago
6 0

Given expression: (256x^{16})^{1/4}.

\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n

=256^{\frac{1}{4}}\left(x^{16}\right)^{\frac{1}{4}}

256=4^4

256^{\frac{1}{4}}=\left(4^4\right)^{\frac{1}{4}}=4

\left(x^{16}\right)^{\frac{1}{4}}=x^{16\cdot \frac{1}{4}}=x^4

(256x^{16})^{1/4} =4x^4

<h3>Therefore, correct option is B option : B.4x^4</h3>
iren2701 [21]3 years ago
3 0

Answer:  The correct option is (B) 4x^4.

Step-by-step explanation:  We are given to select the correct expression that is equivalent to the expression below:

E=(256x^{16})^\frac{1}{4}.

We will be using the following properties of exponents:

(i)~(a^b)^c=a^{b\times c},\\\\(ii)~(ab)^c=a^cb^c.

We have

E\\\\=(256x^{16})^\frac{1}{4}\\\\=(4^4x^{16})^\frac{1}{4}\\\\=(4^4)^\frac{1}{4}(x^{16}^\frac{1}{4})\\\\=4^{4\times\frac{1}{4}}x^{16\times\frac{1}{4}}\\\\=4x^4.

Therefore, the required equivalent expression is 4x^4.

Thus, (B) is the correct option.

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