Exponents and Indices

Evaluate $3^{4}$.

Evaluate $12^{0}$.

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

Simplify $\dfrac{x^{10}}{x^{4}}$.

Simplify $(x^{4})^{3}$.

Simplify $(5 x^{2})^2$.

Write $5^{-2}$ as a fraction.

Write $45000$ in standard form (scientific notation).

Write $0.00007$ in standard form.

Write $6.3 \times 10^{3}$ as an ordinary number.

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

Simplify $\dfrac{18 x^{8}}{3 x^{2}}$.

Simplify $\left(\dfrac{x^{7}}{x^{3}}\right)^{2}$.

Simplify $x^{7} \times x^{-4}$.

Write $\dfrac{1}{x^{6}}$ using a negative index.

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

Calculate $\dfrac{9 \times 10^{5}}{3 \times 10^{2}}$ in standard form.

Simplify $\dfrac{x^{6} \times x^{2}}{x^{5}}$.

How many times larger is $6 \times 10^{8}$ than $2 \times 10^{4}$?

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

Evaluate $81^{1/2}$.

Evaluate $64^{1/3}$.

Evaluate $27^{2/3}$.

Evaluate $49^{-1/2}$.

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

Calculate $(4 \times 10^{6}) + (2 \times 10^{5})$ in standard form.

Simplify $(27)^{-2/3}$.

Solve $2^x = 128$.

If $x = \dfrac{2}{3}$, evaluate $x^{3}$.

Write $\sqrt[5]{x^{3}}$ using a fractional index.

Solve $2^{x+1} = 64$.

Solve $3^{2x} = 729$.

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

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 $\dfrac{x^{4} \cdot y^{-3}}{x^{-2} \cdot y^{5}}$, expressing the answer with positive indices.

Evaluate $(81)^{3/4}$.

Light travels at $3 \times 10^8$ m/s. Calculate the distance light travels in $200$ seconds, in standard form.

Solve $2^{x} \cdot 2^{x+1} = 128$.

Simplify $\left(\dfrac{3x^{4}y^{5}}{x^{1}y^{2}}\right)^{2}$.

Solve $x^{1/3} = 5$ for positive $x$.