Question

please answer this question with steps​

Answer 1

Step-by-step explanation:

= (3⁵-⁸)×3-⁵

= 3³×3-⁵= 3-²

Hope this helps...

Answer 2

Required Answer:

$\underline{\bf{\bullet \: Given:-}}$

$\bf{( 3^5 \div 3^8)^5 \times 3^{-5}}$

$\underline{\bf{\bullet \: What \: To \: Do:-}}$

We have to simplify the expression.

$\underline{\bf{\bullet \: Solution:-}}$

$( 3^5 \div 3^8)^5 \times 3^{-5}$

Also written as,

$\Rightarrow \bigg( \dfrac{3^5}{ 3^8} \bigg)^5 \times 3^{-5}$

Since the powers are the same in brackets.

$\Rightarrow ( 3^{5-8})^5 \times 3^{-5}$

Subtract the powers in brackets,

$\Rightarrow ( 3^{-3})^5 \times 3^{-5}$

Multiply -3 by 5,

$\Rightarrow 3^{-15} \times 3^{-5}$

Since the powers are the same,

$\Rightarrow 3^{-15+ (-5)}$

Add the powers,

$\Rightarrow 3^{-20}$

Since there is a negative sign in the exponent,

$\Rightarrow \dfrac{1}{3^{20}}$

$\boxed{\bf \therefore Thus, the \: answer \: is \: \dfrac{1}{3^{20}}.}$

$\underline{\bf{\bullet \: Laws \: of \: Exponent:-}}$

$1. \: a^m \times a^n = a^{m+n} \\ 2. \: (a^m)^n = a^{mn} \\ 3. \: (ab)^n = a^n b ^n \\ 4. \: \bigg( \dfrac{a}{b} \bigg) ^n = \dfrac{a^n}{b^n} \\ 5. \: a^m \div a^n = a^{m - n} \\ 6. \: a^{-1} = \dfrac{1}{a} \\ 7. \: a^{-m} = \dfrac{1}{a^{m}} \\ 8. \: a^1 = a \\ 9. \: a^0 = 1$