9 (a) Express $$\sqrt{10^{100} \times 10^{100}}$$ as a power of 10 (b) Liam was asked to express $(12^y)$ as a power of 12 Liam wrote $(12^y) = 12^2 = 12^{2y}$ - Edexcel - GCSE Maths - Question 10 - 2022 - Paper 3

To express $\sqrt{10^{100} \times 10^{100}}$ as a power of 10, we first apply the property of square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$. Hence,

$\sqrt{10^{100} \times 10^{100}} = \sqrt{10^{100}} \times \sqrt{10^{100}}$

Now, using the property of square roots that states $\sqrt{10^n} = 10^{\frac{n}{2}}$, we can write:

$\sqrt{10^{100}} = 10^{\frac{100}{2}} = 10^{50}$

Thus,

$\sqrt{10^{100} \times 10^{100}} = 10^{50} \times 10^{50}$

Finally, applying the property of exponents that states $a^m \times a^n = a^{m+n}$, we have:

$10^{50} \times 10^{50} = 10^{50 + 50} = 10^{100}$.