Question

(5x10^ 3)x(9x10^a)=4.5x10^6

Answer 1

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

Answer 2

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`