Write the following using index notation: 3 \times u \times u \times u \times 5 \times v \times v \times v
Simplify the following:
2^{2} \times 2^{2}
4 y^{3} \times 6 y
\left( \dfrac{7}{5} \right)^{m} \times \left( \dfrac{7}{5} \right)^{n}
\dfrac{x^{6}}{3 x^{4}}
\dfrac{4 n^{3} \times 4 n^{4}}{16}
\dfrac{u^{ 2 x + 1}}{u^{x}}
p^{18} \div p^{8} \div p^{5}
m^{9} \div m^{5} \times m^{4}
Rewrite the following expressions without brackets:
\left(\dfrac{a}{b}\right)^{3}
\left(\dfrac{1}{b}\right)^{3}
\left(\dfrac{-1}{2a}\right)^{2}
\left( - \dfrac{5 a}{2} \right)^{3}
Write the following as a single power of 3:
Complete the statement below:
15 j^{14} \div \left(⬚\right) = 5 j^{7}
Simplify the following:
\left(w^{3}\right)^{4}
\left( 3 y^{6}\right)^{2}
\left(u^{x + 1}\right)^{3}
\left( 2 y^{4}\right)^{2} \times \left( 2 y^{2}\right)^{3}
\dfrac{\left(x^{3}\right)^{2}}{x^{3}}
\left( 2^{3} \div 3^{2}\right)^{3}
\dfrac{3^{ 4 a + 2} \times 3^{1 + 6 a}}{\left(3^{3}\right)^{ 3 a - 1}}
\dfrac{81^{ 7 a - 4} \times 9^{ 3 a + 2}}{27^{3 - 3 a}}
Write the following as a single power of 2:
Find the value of a and b in the following equation:
\dfrac{v^{18}}{w^{24}} = \left(\dfrac{v^a}{w^{4}}\right)^b
Write \left(16^{p}\right)^{4} in the form a^b, where a is a prime number.
Use index laws to simplify the ratio \left(0.3\right)^{a}:\left(0.3\right)^{a + 2} to a ratio of whole numbers.
Express 165^{m} as the product of prime bases. Leave your answer in expanded index form.
Find the next term in the sequence\left( 2 x^{2}\right)^{2}, \left( 2 x^{2}\right)^{3},\left( 2 x^{2}\right)^{4}, \left( 2 x^{2}\right)^{5} \ldots
Leave your answer in the form a^{m} b^{n}.
A computer is downloading data at a rate of 3 t^{3} bytes per second. If it downloads 6 \left(t^{3}\right)^{5} bytes, find an expression for the number of seconds the download took. Leave your answer in simplest index form.
Write the following as rational numbers in simplest form:
Write the following as a single power of 2:
Simplify the following, giving your answers with a positive index:
m^{2} \times m^{ - 7 }
\left( 4 m^{ - 10 }\right)^{4}
\left( 4 m^{ - 8 }\right)^{ - 3 }
\dfrac{12 x^{3}}{4 x^{7}}
\left(\dfrac{2 h}{3}\right)^{ - 4 }
Simplify the following, giving your answers with a negative index:
Express the fraction \dfrac{m}{n^{4}} as a product using negative indices.
Express the reciprocal of 8^{9} in:
Positive index form
Negative index form
State whether the following expressions are positive, negative or zero:
If p > 0 and q < 0, which of the following statements is correct?
p^{ - 2 } < 0
- 2 q^3 < 0
q^{ - 2 } < 0
- \left(2 p\right)^2 < 0
Complete the statement below:
32^{ - 6 } = \left( 2^{2} \times \left(⬚\right)^{2}\right)^{ - 3 }
Simplify the following:
a^{0}
\left( 2 \times 13\right)^{0}
\left( 13 x^{7}\right)^{0} + 13^{0} - 13 h^{0}