Question

) Which expressions are equivalent to 35? Choose ALL that apply.
9.27
81.3
3.5
3.3.3.3.3
9.9

Answer 1

Answer:

$(a)\ 9 * 27$

$(b)\ 81 * 3$

$(d)\ 3*3*3*3*3$

Step-by-step explanation:

Given

$3^5$

Required

Select equivalent expressions

$(a)\ 9 * 27$

Express as exponents

$9 * 27 = 3^2 * 3^3$

Apply law of indices

$9 * 27 = 3^{2+3$

$9 * 27 = 3^{5$

$(b)\ 81 * 3$

Express as exponents

$81 * 3 = 3^4 * 3$

Apply law of indices

$81 * 3 = 3^{4+1$

$81 * 3 = 3^5$

$(c)\ 3*5$

Solve

$3*5 = 15$

$(d)\ 3*3*3*3*3$

From calculator, we have

$3*3*3*3*3=243$

Express as exponents

$3*3*3*3*3=3^5$

$(e) 9 * 9$

Express as exponents

$9 * 9= 3^2 * 3^2$

Apply law of indices

$9 * 9= 3^{2+2$

$9 * 9= 3^4$

Hence, a, b and d are true