Question

Which is equivalent to 16^3/4x

Answer 1

I used a photo to reduce confusion. When solving fractional indices, the numerator becomes the power and the denominator becomes the root. Hope this helps.

Answer 2

Answer:

The given expression is equivalent to $(\sqrt[4]{16})^{3x}$ or $8^x$.

Step-by-step explanation:

The given expression is

$16^{\frac{3}{4}x}$

Use the property of exponent ,

$x^{mn}=(x^m)^n$

$16^{\frac{3}{4}x}=(16^\frac{1}{4})^{3x}$

Use the property of radical expression,

$x^{\frac{1}{n}}=\sqrt[n]{x}$

$16^{\frac{3}{4}x}=(\sqrt[4]{16})^{3x}$

Therefore the given expression is equivalent to $(\sqrt[4]{16})^{3x}$.

After more simplification we get,

$16^{\frac{3}{4}x}=2^{3x}$

$16^{\frac{3}{4}x}=8^x$

Therefore the given expression is also equivalent to $8^x$.