83.4k views
5 votes
(5x10^ 3)x(9x10^a)=4.5x10^6

2 Answers

2 votes

Answer:

a = 2

Explanation:

(5 × 10³) × (9 × 10ᵃ) = 4.5 × 10⁶

(5 × 9) × (10³ × 10ᵃ) = 4.5 × 10⁶

45 ×
10^(3 + a) = 4.5 × 10⁶

4.5 ×
10^(3 + a + 1) = 4.5 × 10⁶


10^(4 + a) = 10⁶

4 + a = 6

a = 2

User Morphyish
by
8.1k points
4 votes

Answer:

a = 2

Explanation:

Given equation:


(5 * 10^3)(9 * 10^a)=4.5 * 10^6

Divide both sides of the equation by 5 × 10³:


\implies 9 * 10^a=(4.5 * 10^6)/(5 * 10^3)


\textsf{Simplify the right side of the equation by dividing the numbers $4.5$ and $5$,}\\\\\textsf{and applying the exponent rule: \quad $\boxed{(a^b)/(a^c)=a^(b-c)}$}


\implies 9 * 10^a=0.9 *10^(6-3)


\implies 9 * 10^a=0.9 *10^3

Divide both sides of the equation by 9:


\implies 10^a=0.1 *10^3

Simplify the right side of the equation:


\implies 10^a=1*10^2


\implies 10^a=10^2


\textsf{Apply the exponent rule:} \quad a^(f(x))=a^(g(x)) \implies f(x)=g(x)


\implies a = 2

User Edgar Derby
by
8.2k points

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