Remake it in English

Since the first digit after the decimal (8) is 5 or greater, round up.

Answer: $\boxed{\text{37}}$

b)

Since the first digit after the decimal (5) is 5 or greater, round up.

Answer: $\boxed{\text{2017}}$

c)

Since the first digit after the decimal (1) is less than 5, round down.

Answer: $\boxed{\text{7}}$

Write the following numbers in index form (simplify using index laws):

• $3^{17} \times 3^6$

$$
3^{23}
$$
Answer: $\boxed{3^{23}}$

• $a^{23} \times a^{10}$

$$
a^{33}
$$
Answer: $\boxed{a^{33}}$

• $24a^7 \div 6a^3$

$$
4a^4
$$
Answer: $\boxed{4a^4}$

Simplify by removing fractions (fractional indices):

a)

• $81^{\frac{1}{4}}$

$a^{\frac{1}{n}} = \sqrt[n]{a}$. $\sqrt[4]{81}$

$$
3^4 = 81
$$
Answer: $\boxed{3}$

• $(cx^3)^{\frac{4}{3}}$

$(ab)^n = a^n b^n$. $c^{\frac{4}{3}} \times (x^3)^{\frac{4}{3}}$

$(a^m)^n = a^{mn}$. $c^{\frac{4}{3}} \times x^{3 \times \frac{4}{3}}$

$$
c x^4 \sqrt[3]{c}
$$
Answer: $\boxed{cx^4\sqrt[3]{c}}$

d)

• $9^{\frac{1}{2}}$

$a^{\frac{1}{n}} = \sqrt[n]{a}$. $\sqrt{9}$

$$
3
$$
Answer: $\boxed{3}$

• $(z^3)^{\frac{1}{3}}$

$(a^m)^n = a^{mn}$. $z^{3 \times \frac{1}{3}}$