How do you simplify ${(\frac{4 x^{4}}{y^{7}})}^{4}$ $(\frac { 4x ^ { 4} } { y ^ { 7} } ) ^ { 4}$ ?

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Answer 1 · 2017-04-27T03:04:21

$\frac{256 x^{16}}{y^{28}}$ $[256x^(16)]/(y^(28))$

This can be written as...

$\frac{{(4)}^{4} {(x^{4})}^{4}}{{(y^{7})}^{4}}$ $[(4)^4(x^4)^4]/(y^7)^4$

We know by properties of exponents that when you have an exponent raised to another exponent you can multiply them and get the same result

$\frac{{(4)}^{4} (x^{4 \cdot 4})}{(y^{7 \cdot 4})}$ $[(4)^4(x^(4*4))]/((y^(7*4)))$

Now we can multiply the exponents and raise $4$ $4$ to the fourth power to get our answer

$\frac{256 x^{16}}{y^{28}}$ $color(green)[[256x^(16)]/(y^(28))]$

How do you simplify (4x4y7)4(\frac { 4x ^ { 4} } { y ^ { 7} } ) ^ { 4}?