Question

not all items in the item bank will be used.

the expressions above (and the ones on the left) seem to be for matching. the top row has: (\frac{9b_6}{b_4}), (b_5 cdot b_6 cdot b_2), (\frac{8b_6}{2b_4}), (b_5 cdot b_6), (\frac{9b_7}{b_4})
the bottom (dashed) row has: (empty), (b_{13}), (empty), (b_{11}), (9b_3)
on the left, there are items like (b_{30}), (b_{60}), (9b_{1.5}), (9b_2), (4b_{1.5}), (4b_2)

Explanation:

Step1: Simplify $\frac{9b^7}{b^4}$

Subtract exponents: $9b^{7-4}=9b^3$

Step2: Simplify $b^5 \cdot b^6$

Add exponents: $b^{5+6}=b^{11}$

Step3: Simplify $\frac{8b^6}{2b^4}$

Divide coefficients, subtract exponents: $\frac{8}{2}b^{6-4}=4b^2$

Step4: Simplify $b^5 \cdot b^6 \cdot b^2$

Add exponents: $b^{5+6+2}=b^{13}$

Step5: Simplify $\frac{9b^6}{b^4}$

Subtract exponents: $9b^{6-4}=9b^2$

Answer:

• $\boldsymbol{\frac{9b^7}{b^4}

ightarrow 9b^3}$

• $\boldsymbol{b^5 \cdot b^6

ightarrow b^{11}}$

• $\boldsymbol{\frac{8b^6}{2b^4}

ightarrow 4b^2}$

• $\boldsymbol{b^5 \cdot b^6 \cdot b^2

ightarrow b^{13}}$

• $\boldsymbol{\frac{9b^6}{b^4}

ightarrow 9b^2}$