9.7 Indices and Scientific Notation

Evaluate $2^5$.

Write $3^2 \times 3^5$ as a single power of $a$.

Write $\dfrac{a^p}{a^q}$ as a single power.

Write 32000 in standard form.

Write the decimal 0.004 in standard form.

Evaluate $(7)^0$ and $(7)^{-2}$.

Write $(a^p)^q$ as a single power.

Simplify $x^p \times x^q$.

Write 0.5 × 10⁵ in standard form.

Evaluate $5^0$ and $5^1$.

Simplify $(a \times 10^p) \times (b \times 10^q)$.

Simplify $\dfrac{a \times 10^p}{b \times 10^q}$.

Simplify $\dfrac{x^p}{x^q}$.

Evaluate $a^{1/2}$.

Write $35 \times 10^5$ in standard form.

Compute $5 \times 10^4 + 3 \times 10^3$ in standard form.

Evaluate $a^{-1}$.

Simplify $(2x)^3$.

Convert: a light-year ≈ $9.5 \times 10^{12}$ km. Express in metres.

Compute $(2 \times 10^3)^2$.

Simplify $\dfrac{(x^p)^q}{x^r}$.

Write $35 \times 10^5$ in standard form.

Evaluate $a^{1/2}$ where a = 25.

UK population was $6.50 \times 10^7$ in 2016, growing 0.6% per year. Estimate the 2020 population (3 s.f.).

Compute $(3 \times 10^4) \times (4 \times 10^{-2})$ in standard form.

Convert $a \times 10^p$ to ordinary: $3.6 \times 10^{-3}$.

Evaluate $a^{2/3}$ where a = 8.

Compute $\dfrac{6 \times 10^7}{2 \times 10^4}$ in standard form.

Simplify $(2x^3)^2 \times (3x)^2$.

Order from smallest to largest: $3 \times 10^{-3}, 2 \times 10^{-4}, 4 \times 10^{-3}$.

Solve $x^p = {rhs}$.

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

A nearby star is $4.2$ light-years away. 1 light-year ≈ $9.46 \times 10^{12}$ km. Find distance in km (3 s.f.).

Solve $x^{1/3} = n$.

A bacteria culture starts at $2.5 \times 10^4$ cells, doubling every hour. (a) After 1 hour. (b) After 5 hours. (c) When does it exceed $10^8$?

Evaluate $27^{-2/3}$.

Solve $2^x = 32$.

Solve $x^4 = 81$ for real $x$.

Express $\sqrt[3]{27 a^9}$ in simplified index form.

Compute $(10^3)^{1/3}$ and $(10^6)^{1/3}$.