Asha worked out $$rac{326.8 imes (6.94 - 3.4)}{59.4}$$ She got an answer of 19.5, correct to 3 significant figures - OCR - GCSE Maths - Question 21 - 2018 - Paper 1

To show that:

$a^5 \times (a^2)^2$ can be rewritten as $a^{11}$,

we start by applying the power rule of exponents:

1. First, simplify $(a^2)^2$:

   $(a^2)^2 = a^{2 \times 2} = a^4$

2. Now substitute back into the expression:

   $a^5 \times a^4$

3. According to the product rule of exponents:

   $a^m \times a^n = a^{m+n}$ So, we have:

   $a^5 \times a^4 = a^{5+4} = a^{9}$

Thus, the expression simplifies to not $a^{11}$, which means Asha needs to review her calculation, as it's a mistake in interpretation as per the task; she should express it correctly as $a^{9}$.

To express:

$\frac{1}{125} \times 2^{59}$ as a power of 5:

1. First, recognize that $125$ is equal to $5^3$.

2. Thus, we can rewrite:

   $\frac{1}{125} = \frac{1}{5^3} = 5^{-3}$

3. Therefore, substituting this back into our original expression gives:

   $5^{-3} \times 2^{59}$

This expression cannot be entirely expressed as a power of 5 while maintaining equality, unless you specify how to link $2^{59}$ in terms of base 5 if needed for other comparisons.