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Exercise

$\sqrt{10^{3x}}$

Step-by-step Solution

1

Simplify $\sqrt{10^{3x}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $3x$ and $n$ equals $\frac{1}{2}$

$10^{3\cdot \left(\frac{1}{2}\right)x}$
2

Multiply the fraction and term in $3\cdot \left(\frac{1}{2}\right)x$

$10^{\frac{3\cdot 1}{2}x}$
3

Multiply $3$ times $1$

$10^{\frac{3}{2}x}$

Final answer to the exercise

$10^{\frac{3}{2}x}$

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Similar Questions Solved

$\sqrt[4]{x^3}$

$\left(2^3\right)^2$

$\left(5^3\right)^4$

$\sqrt[3]{x^3}$

$\left(2^2\right)^4$

$\left(3^2\right)^3$

$\sqrt[5]{x^3}$

Main Topic: Powers of powers

When we have a power inside another power, we can simplify multiplying the exponents: $\left(x^m\right)^n=x^{m\cdot n}$.

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