$\log_{ 10 }({ 25 })+\log_{ 10 }({ {8}^{-\frac{ 1 }{ 3 }} })+3\log_{ 10 }({ 2 })$
Use $x \times \log_{ a }({ b })=\log_{ a }({ {b}^{x} })$ to transform the expression$\log_{ 10 }({ 25 })+\log_{ 10 }({ {8}^{-\frac{ 1 }{ 3 }} })+\log_{ 10 }({ {2}^{3} })$
Use the logarithmic product and quotient rules to simplify the expression$\log_{ 10 }({ 25 \times {8}^{-\frac{ 1 }{ 3 }} \times {2}^{3} })$
Express with a positive exponent using ${a}^{-n}=\frac{ 1 }{ {a}^{n} }$$\log_{ 10 }({ 25 \times \frac{ 1 }{ {8}^{\frac{ 1 }{ 3 }} } \times {2}^{3} })$
Write the number in exponential form with the base of $2$$\log_{ 10 }({ 25 \times \frac{ 1 }{ {\left( {2}^{3} \right)}^{\frac{ 1 }{ 3 }} } \times {2}^{3} })$
Simplify the expression by multiplying exponents$\log_{ 10 }({ 25 \times \frac{ 1 }{ 2 } \times {2}^{3} })$
Cancel out the common factor $2$$\log_{ 10 }({ 25 \times {2}^{2} })$
Evaluate the power$\log_{ 10 }({ 25 \times 4 })$
Multiply the numbers$\log_{ 10 }({ 100 })$
Write the number in exponential form with the base of $10$$\log_{ 10 }({ {10}^{2} })$
Use $\log_{ a }({ {a}^{x} })=x$ to simplify the expression$2$