Simultaneous Equations with Exponents

You are given the terms $a^{3}b^{2}c$ and $bc^2$ . If you multiply these variables together like shown below, you receive the expression ( $a^{3}b^{3}c^{3}$ ), which will be equal to the value of the product of the variables you multiplied together ( $1 \times 8$ ). $a^{3}b^{2+1}c^{1+2}=8 \times 1=8$ You now have: $a^{3}b^{3}c^{3}=8$ Take the cube root of $a^{3}b^{3}c^{3}=8$ to receive $abc=2$ . The answer is $\boxed{2}$ .

$a^3b^2c=8$ $\color{#D61F06}(1)$

$bc^2=1$ $\color{#D61F06}(2)$

Multiply $\color{#D61F06}(1)$ and $\color{#D61F06}(2)$ , we get

$a^3b^3c^3=8$

Extracting the cube root of both sides, we get

$abc=$ $\large{\color{plum}\boxed{2}}$