Problem solving with the laws of indices | Maths | Quizalize & Oak National Academy

Starter quiz

Evaluate $16^\frac{1}{2}$ , giving the positive solution where necessary.

'4' ✓
Evaluate $9^\frac{3}{2}$ , giving the positive solution where necessary.

'27' ✓
Evaluate $25^\frac{1}{2}$ , giving the positive solution where necessary.

'5' ✓
What is the value of $b$ for $b^7 \div b^5 =9^2$ ?

'9' ✓
What is the value of $k$ for $0.2^5 \div 0.2^k = 0.2^7$ ?

'-2' ✓
What number is written as $2^3 \times 5 \times 7$ as a product of its prime factors?

'280' ✓

What is the value of $x$ for $(3^3)^4 \times 3^2 = 3^x$ ?

'14' ✓
What is the value of $x$ for $\frac{2^{12} \times 2^4}{2^{10}} = 2^x$ ?

'6' ✓
What is the value of $x$ for $\frac{5^{14} \times 5^5}{5^{-2}} = 5^x$ ?

'21' ✓
What is the value of $x$ for $3^2 \times 3^6 = 9^x$ ?

'4' ✓
What is the value of $x$ for $2^3 \times 4^3 = 2^x$ ?

'9' ✓
What is the value of $x^{4x}$ for $2^x \times 2^{3x} = x^{4x}$ ?

'256' ✓

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The base could be a number, letter or combination of the two.
The laws are another way you can simplify an expression.
Plotting numbers against their squared values can help you estimate unknown amounts.

Using the laws of indices, when dividing by a number with a negative exponent pupils can incorrectly subtract the negative exponent.

When the bases of all the numbers are the same, forming an equation with the exponents can reduce errors.

Power - An alternative word for exponent or index. Used when reading exponents above 3. E.g. 2^4 is read as “2 to the power of 4”.
Vinculum - Vinculum is the horizontal line placed over an expression to show that everything below that line is one group.