Solve 12text{yr}(b)14yrquadtext{(c)}16yrquadtext{(d)}24yr

$$12 \text { yr } ( b ) 14 y r \quad \text { (c) } 16 y r \quad \text { (d) } 24 y r$$

Evaluate

$$64512bcd\left(ry\right)^{4}$$

Solution Steps

Multiply y and y to get y^{2}.

$$12y^{2}rb\times 14rc\times 16yrd\times 24yr$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$12y^{3}rb\times 14rc\times 16rd\times 24yr$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$12y^{4}rb\times 14rc\times 16rd\times 24r$$

Multiply r and r to get r^{2}.

$$12y^{4}r^{2}b\times 14c\times 16rd\times 24r$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$12y^{4}r^{3}b\times 14c\times 16d\times 24r$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$12y^{4}r^{4}b\times 14c\times 16d\times 24$$

Multiply 12 and 14 to get 168.

$$168y^{4}r^{4}bc\times 16d\times 24$$

Multiply 168 and 16 to get 2688.

$$2688y^{4}r^{4}bcd\times 24$$

Multiply 2688 and 24 to get 64512.

$$64512y^{4}r^{4}bcd$$

Differentiate w.r.t. b

$$64512cd\left(ry\right)^{4}$$