Rewrite each expression in simplest form.

$(a) 6 \times x \times y$
$(b) 7 \times a \times b$
$(c) x \times y \times z$
$(d) 2 \times y \times y$
$(e) a \times 4 \times b$
$(f) x \times y \times 12$
$(g) 5 \times b \times a$
$(h) y \times z \times z$

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a) 6 xy    b) 7 ab  c) xyz    d) 2 y^{2} e) 4 ab   f) 12 xy    g) 5 ab    h) y z^{2}

a) 5 xy    b) 8 ab  c) xyz    d) 3 y^{2} e) 4 ab   f) 18 xy    g) 5 ab    h) y z^{2}

a) 4 xy    b) 9 ab  c) xyz    d) 6 y^{2} e) 4 ab   f) 13 xy    g) 5 ab    h) y z^{2}

a) 2 xy    b) 2 ab  c) xyz    d) 4 y^{2} e) 4 ab   f) 15 xy    g) 5 ab    h) y z^{2}

answer is A.

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Detailed Solution

Concept: Applying the BODMAS rule, simplify each of the given algebraic expressions. Use the exponents law, which says that

a^{b \times} a^{c} = a^{b + c} and \frac{a^{b}}{a^{c}} = a^{b - c}

Remember that if two terms share the same variable, their coefficients can be added or subtracted.
Each of the algebraic expressions that are supplied must be simplified.
To do this, we shall adhere to the laws of exponents and BODMAS, which declare that

a^{b \times} a^{c}

a^{b + c}

and

\frac{a^{b}}{a^{c}}

a^{b - c}

Only when both terms share the same variables may we add or subtract the coefficients of the two terms.
We will now make each of the options more straightforward.
(a) We can rewrite the phrase

6 xy

by multiplying all of its terms.
(b) We can rewrite the expression

7 ab

by multiplying all of the terms in it.
(c) We can recast the phrase

xyz

by multiplying all of its terms.
(d) We can rewrite the expression

2 y^{2}

by multiplying all of its terms.
(d) We can rewrite the phrase a 4 b as 4ab by multiplying all of its terms.
(f) We can rewrite the expression xy12 as