How do you simplify ${(\sqrt{x + 9})}^{4} \cdot {(\sqrt{x + 9})}^{99}$ $(sqrt(x +9))^4* (sqrt(x+9))^99$ ?

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Answer 1 · 2017-10-28T07:01:18

${(\sqrt{x + 9})}^{4} \cdot {(\sqrt{x + 9})}^{99} = {(x + 9)}^{\frac{103}{2}}$ $(sqrt(x+9))^4 * (sqrt(x+9))^99 = (x+9)^(103/2)$

${(\sqrt{x + 9})}^{4} \cdot {(\sqrt{x + 9})}^{99}$ $(sqrt(x+9))^4 * (sqrt(x+9))^99$

$Apply exponent rule (x^{a} \times x^{b} = x^{a + b})$ $"Apply exponent rule" (x^a xx x^b = x^(a+b))$

${(\sqrt{x + 9})}^{4} \cdot {(\sqrt{x + 9})}^{99} = {(\sqrt{x + 9})}^{103}$ $(sqrt(x+9))^4 * (sqrt(x+9))^99 = (sqrt(x+9))^103$

$\sqrt{x} = x^{\frac{1}{2}}$ $color(blue)( sqrtx = x^(1/2)$

${(\sqrt{x + 9})}^{103} = {({(x + 9)}^{\frac{1}{2}})}^{103}$ $(sqrt(x+9))^103 = ((x+9)^(1/2))^103$

$= {(x + 9)}^{\frac{1}{2} \times 103}$ $= (x+9)^(1/2 xx 103)$

$= {(x + 9)}^{\frac{103}{2}}$ $= (x+9)^(103/2)$

$or$ $"or"$
$= {(x + 9)}^{51.5}$ $= (x+9)^(51.5)$

How do you simplify (√x+9)4⋅(√x+9)99(sqrt(x +9))^4* (sqrt(x+9))^99?