Exponents and Indices

Evaluate $2^{5}$.

Evaluate $7^{0}$.

Simplify $x^{3} \times x^{4}$.

Simplify $\dfrac{x^{8}}{x^{3}}$.

Simplify $(x^{3})^{2}$.

Simplify $(2 x^{3})^2$.

Write $2^{-3}$ as a fraction.

Write $3000$ in standard form (scientific notation).

Write $0.004$ in standard form.

Write $2.5 \times 10^{4}$ as an ordinary number.

Simplify $3 x^{2} \times 4 x^{5}$.

Simplify $\dfrac{20 x^{7}}{4 x^{3}}$.

Simplify $\left(\dfrac{x^{5}}{x^{2}}\right)^{3}$.

Simplify $x^{5} \times x^{-2}$.

Write $\dfrac{1}{x^{4}}$ using a negative index.

Calculate $(3 \times 10^{4}) \times (2 \times 10^{5})$, giving your answer in standard form.

Calculate $\dfrac{8 \times 10^{7}}{2 \times 10^{3}}$ in standard form.

Simplify $\dfrac{x^{4} \times x^{3}}{x^{2}}$.

How many times larger is $6 \times 10^{7}$ than $2 \times 10^{3}$?

Simplify $(-3 x^{2})^{2}$.

Evaluate $25^{1/2}$.

Evaluate $27^{1/3}$.

Evaluate $8^{2/3}$.

Evaluate $16^{-1/2}$.

Simplify $\dfrac{(2 x^{3})^{2}}{x^{4}}$.

Calculate $(3 \times 10^{5}) + (5 \times 10^{4})$ in standard form.

Simplify $(8)^{-2/3}$.

Solve $2^x = 32$.

If $x = \dfrac{1}{2}$, evaluate $x^{4}$.

Write $\sqrt[3]{x^{2}}$ using a fractional index.

Solve $2^{x+1} = 32$.

Solve $3^{2x} = 81$.

Simplify $\dfrac{(2 x^{3})^{2} \cdot x^{5}}{x^{4}}$.

The mass of Earth is $6 \times 10^{24}$ kg and the mass of the Sun is $2 \times 10^{30}$ kg. How many times more massive is the Sun?

Simplify $\dfrac{x^{3} \cdot y^{-2}}{x^{-1} \cdot y^{4}}$, expressing the answer with positive indices.

Evaluate $(16)^{3/4}$.

Light travels at $3 \times 10^8$ m/s. Calculate the distance light travels in $600$ seconds, in standard form.

Solve $2^{x} \cdot 2^{x+1} = 32$.

Simplify $\left(\dfrac{2x^{5}y^{3}}{x^{2}y^{1}}\right)^{2}$.

Solve $x^{1/3} = 4$ for positive $x$.