Question

Simplify (5²⁰ ÷ 5¹¹) × 5⁴ and write in exponential form

Answer 1

Answer:

if the base is same in division the power will subtracted so 20-11=9 5 raise to the power 9 then in multiplication if base is same the power will add so 5 to the power 9 and 5 to the power 4 it will become 5 raise to the power 13.

Answer 2

Answer :-

( 5²⁰ ÷ 5¹¹ ) × 5⁴ = 5¹³

EXPLANATION

To Find :-

• Simplify (5²⁰ ÷ 5¹¹) × 5⁴

★ Solution

⇒ (5²⁰ ÷ 5¹¹) × 5⁴

By using the law of exponent,

[xᵐ/xⁿ = xᵐ⁻ⁿ],

⇒ (5²⁰⁻¹¹) × 5⁴

By subtracting 11 from 20, [20 - 11],

⇒ (5⁹) × 5⁴

By using the law of exponent,

[xᵐ·xⁿ = xᵐ⁺ⁿ],

⇒ 5⁹⁺⁴

By adding 9 and 4, [9 + 4],

⇒ 5¹³ ★

Hence, ( 5²⁰ ÷ 5¹¹ ) × 5⁴ is 5¹³.

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LAWS OF EXPONENTS used :-

• xᵐ ÷ xⁿ = xᵐ⁻ⁿ
• (xᵐ)*(xⁿ) = xᵐ⁺ⁿ

More Information :-

Few more information related to exponents,

• (xᵐ)ⁿ = xᵐⁿ
• xᵐxⁿ = xᵐ⁺ⁿ
• (xy)ⁿ = xⁿyⁿ
• (x/y)ⁿ = xⁿ/yⁿ
• xᵐ/xⁿ = 1/xⁿ⁻ᵐ